For your senior project, you would like to build a cyclotron that will accelerate protons to 10% of the speed of light. The largest vacuum chamber you can find is 60 cm in diameter.

Consider the particle-in-a-box problem in 1d. a particle with mass m is confined to move freely between two hard walls situated at x = 0 and x = l. the potential energy function is given as (a) describe the boundary conditions that must be satisfied by the wavefunctions ψ(x) (such as energy eigenfunctions). (b) solve the schr¨odinger’s equation and by using the boundary conditions of part (a) find all energy eigenfunctions, ψn(x), and the corresponding energies, en. (c) what are the allowed values of the quantum number n above? how did you decide on that? (d) what is the de broglie wavelength for the ground state? (e) sketch a plot of the lowest 3 levels’ wavefunctions (ψn(x) vs x). don’t forget to mark the positions of the walls on the graphs. (f) in a transition between the energy levels above, which transition produces the longest wavelength λ for the emitted photon? what is the corresponding wavele

7. see worksheet 1 for values of variables x1, x2 and x3 and answer the following questions: a. for each variable find the mean, median, coefficient of skewness, range and population standard deviation. b. compared to variable x1, how are the mean and median affected by extreme values (outliers) seen in x2 and x3. c. is the median or mean the better measure of location for x2 and x3? explain. d. explain the differences in the magnitudes of the skewness coefficients for the three variables. e. what is the relationship between the range and standard deviation looking across the three variables?

Sally turns on her cellular telephone to speak to her friend who is located thousands of miles away. which of the following best describes how such a telephone is able to transmit and receive information? a. the cellular telephone transmits, receives, and encodes information using only sound waves. b. the cellular telephone transmits, receives, and encodes information using only electromagnetic waves. c. the cellular telephone transmits information by electromagnetic waves to a receiver which then encodes them and produces sound. d. the cellular telephone transmits information by sound waves to a receiver which then encodes them and produces electromagnetic waves.